A Bayesian Treatment for Singular Value Decomposition

The traditional Singular Value Decomposition (SVD) based recommendation system suffers from two key challenges, namely, (1) the normal assumption is not an appropriate one since it is sensitive to outliers, which means the predicted mean would be changed a lot from the true value by the presence of outliers, and (2) the penalty terms added on the feature vectors are difficult to be settled in advance and thus an automatic configuring method for setting penalty terms is indispensable. To solve that, we propose a Bayesian based singular value decomposition (BSVD) and its related inference algorithms in this study. Specifically, we impose a T assumption on the ratings and the feature vectors, and propose a Gibbs sampler for the inference part. Besides giving a statistical explanation of the inference part and showing that this procedure is meaningful, we list the results of a series of experiments to further verify the performance of our proposed Bayesian SVD.